[Retros] Distance-PG = Fastest "n"
Francois Labelle
flab at wismuth.com
Mon Aug 29 22:50:10 EDT 2016
So far I reached ply 8 with the checkmate condition, and ply 7 without
conditions. To find all solutions to (a,b,c) I only need to reach ply
a+b+c, which is why I was able to claim that I know all of the solutions
to "checkmate (2,6,0)" and "checkmate (7,1,0)".
In a few days I should have results 1 ply deeper. If needed I can
probably get 1 extra ply deeper with little effort in special cases, for
example if I search uniquely for integer distances (problems of the type
(a,0,0) without any diagonal or knight moves).
François
On 29/08/16 03:32 PM, andrew buchanan wrote:
> Hi Francois,
>
> Thanks for this.
>
> How deep have you plied, please? Just to give us an idea of where it's
> not worth searching.
>
> Cheers,
> Andrew
>
> ------------------------------------------------------------------------
> *From:* Francois Labelle <flab at wismuth.com>
> *To:* andrew buchanan <andrew at anselan.com>; The Retrograde Analysis
> Mailing List <retros at janko.at>
> *Sent:* Monday, August 29, 2016 9:52 PM
> *Subject:* Re: [Retros] Distance-PG = Fastest "n"
>
> Hi Andrew,
>
> The ply number is meant to be part of the stipulation, sorry for not
> having been clear. For the problems I listed it is also possible to
> instead ask for the shortest solution.
>
> An example of a non-shortest problem would be to ask for a checkmate
> of total move length (2,6,0) in 3.5 moves. The solution is unique, 1.
> e3 d6 2. Qe2 Kd7 3. Qd3 Kc6 4. Qb5# , but non-shortest because there
> is also a solution in 3.0 moves: 1. d3 e6 2. Kd2 Qe7 3. Kc3 Qb4# .
>
> For the moment I don't have an example of a problem that is sound
> without specifying the number of moves or asking that it be shortest,
> but "checkmate (2,6,0)" comes close with only the two solutions above
> and nothing else. The problem "checkmate (7,1,0)" is also a close
> call, with 2 solutions in 3.5 moves,
> 1. d3 e6 2. Qd2 e5 3. Qe3 Ke7 4. Qxe5#
> 1. d3 e6 2. Qd2 Ke7 3. Qe3 e5 4. Qxe5#
> and nothing else.
>
> François
>
> On 29/08/16 06:12 AM, andrew buchanan wrote:
>> Hi,
>>
>> I guess the ply number is meant to be part of the stipulation? Or
>> should the stipulation ask for the quickest solution?
>>
>> For example:
>> "find a game with total move length of 6 + 5*sqrt(2) + 0*sqrt(5)
>> ending in checkmate".
>> 1. f4 e5 2. fxe5 Qe7 3. g4 Qh4#
>> In what sense is this ply 6 non-unique solution not a cook of the
>> problem as stated?
>>
>> And on reflection, I think it's nicer *not* to subtract 1 for en
>> passant: because if you do then many problems will be cooked. Good to
>> be able to force en passant in a novel way, without relying on pins etc.
>>
>> Thanks,
>> Andrew
>>
>> ------------------------------------------------------------------------
>> *From:* Eric Angelini <Eric.Angelini at kntv.be>
>> <mailto:Eric.Angelini at kntv.be>
>> *To:* The Retrograde Analysis Mailing List <retros at janko.at>
>> <mailto:retros at janko.at>
>> *Sent:* Monday, August 29, 2016 5:38 PM
>> *Subject:* Re: [Retros] Distance-PG = Fastest "n"
>>
>> Many thanks, François, this is what I was looking for !
>> >length of a + b*sqrt(2) + c*sqrt(5)
>> ... this is what I like too: those a, b and c give just
>> the right amount of information about the game (strait
>> one-square movements, oblique one-square movements, jumps).
>> >tempting to use sqrt(2)-1 to retroactively shrink the previous move.
>> ... brilliant idea !
>> Merci encore !
>> É.
>> *De :*Retros [mailto:retros-bounces at janko.at] *De la part de*
>> Francois Labelle
>> *Envoyé :* dimanche 28 août 2016 21:37
>> *À :* retros at janko.at <mailto:retros at janko.at>
>> *Objet :* Re: [Retros] Distance-PG = Fastest "n"
>> Hi Eric,
>>
>> If I programmed things correctly, then these problems should have
>> unique solutions:
>>
>> ply 5
>> 6,5,0
>>
>> ply 6
>> 2,6,0
>> 3,6,0 (similar to previous)
>> 3,8,0
>> 3,9,0 (similar to previous)
>> 3,10,0 (similar to previous)
>> 3,11,0
>> 6,11,0
>> 8,2,0
>> 9,6,0 (similar to 3,6,0)
>> 10,7,0 (similar to 6,11,0)
>>
>> where a,b,c means "find a game with total move length of a +
>> b*sqrt(2) + c*sqrt(5) ending in checkmate".
>>
>> I also found problems with unique solutions without the "checkmate"
>> condition:
>>
>> ply4
>> 5,0,2
>> 7,4,0
>>
>> ply5
>> 5,5,2
>>
>> ply6
>> 14,9,0
>> 16,6,0
>> 16,7,0
>> 16,8,0
>> 17,5,0
>>
>> For example, the solution to "ply4 5,0,2" is "1. Nc3 d5 2. Nxd5 Qxd5".
>>
>> There's still the question of the length of an e.p. capture. I
>> assumed sqrt(2), blindly using the maximummer definition (see "length
>> of a move" from
>> http://christian.poisson.free.fr/problemesis/condus.html which
>> doesn't say anything special about e.p.). But in this case, because
>> we're adding all the lengths, I admit that it's tempting to use
>> sqrt(2)-1 to retroactively shrink the previous move.
>>
>> François
>> On 28/08/16 12:15 PM, Eric Angelini wrote:
>>
>> The herunder game ending in checkmate
>> has the same length 4(1+SQR2) as
>> the "Black version" seen before:
>> 1. e2 -- g5
>> 2. Be2 -- f6
>> 3. Bh5++
>> But this checkmate is not as fast as
>> the Black's one. So what do "fast"
>> and "fastest" mean? Well, this deals
>> obviously with the quantity of moves.
>> If this type of problem has no name,
>> it could be baptised "Fastest n" --
>> "n" being a quantity in square-side
>> units.
>> At least this type of problem doesn't
>> need any diagram -- what a relief for
>> printed magazines !-))
>>
>> Le 28 août 2016 à 17:08, Eric Angelini <Eric.Angelini at kntv.be
>> <mailto:Eric.Angelini at kntv.be>> a écrit :
>>
>> For instance, the fastest Distance-PG
>> of total length 4(1+SQR2) ending in checkmate comes of course
>> after the
>> well known:
>> 1.f3 -- e6
>> 2.g4 -- Qh4++
>> ... but as the White moves can be
>> exchanged, this is not a unique
>> solution.
>> à+
>> É.
>> Catapulté de mon aPhone
>>
>> Le 28 août 2016 à 16:20, Eric Angelini <Eric.Angelini at kntv.be
>> <mailto:Eric.Angelini at kntv.be>> a écrit :
>>
>> Yes Roberto,
>> a sound proof game of this (total) length,
>> and, in my dreams, the shortest one,
>> hopefully unique, I have in mind.
>> More generally, one can assign for
>> any past, present and future a single
>> such number, if I'm not wrong.
>> It would be nice to have unique
>> numbers "n" for precise tasks like:
>> -find the SPG of total length "n" ending in a checkmate;
>> -find the SPG of total length "n"
>> with a casling;
>> -find the SPG of total length "n"
>> with an en passant capture, etc.
>> BTW, what would be the geometrical
>> length of an e.p. capture?
>> But this is old hat, I'm sure, no?
>> à+
>> É.
>> Catapulté de mon aPhone
>>
>> Le 28 août 2016 à 13:53, roberto osorio
>> <osorio.arg at gmail.com <mailto:osorio.arg at gmail.com>> a
>> écrit :
>>
>> Hi Eric,
>> with SQR5 you surely mean a knight move, so the PG
>> has to include 6 knight moves plus straight
>> displacements total 20 long.
>> Many unsound sequences fit whit these requirements.
>> When you say "Find a PG", do you mean "a sound PG"?
>> best,
>> Roberto Osorio
>> 2016-08-27 10:17 GMT-03:00 Eric Angelini
>> <Eric.Angelini at kntv.be <mailto:Eric.Angelini at kntv.be>>:
>>
>>
>> Hello Retro-fans,
>> This is for sure old hat, but do you know
>> a nicer example than my attempt
>> to produce an unique solution?
>>
>> "Find a PG ending in checkmate where the pieces
>> have browsed
>> the distance of 20 + 6SQR5 units"
>>
>> (read "twenty plus six times the
>> square roots of five" - the unit being
>> the side of a square, of course)
>> Best,
>> É.
>>
>>
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